Deciphering the relevance of a title is like figuring out a puzzle! Undeniably, the question, "What is the sound of one hand clapping?" is a philosophical Zen riddle. King, a teacher of Zen, explains the answer, which is that it makes the same sound as two hands clapping, by saying that

The basic principle states that there are no limits, which implies that everything is in a relationship to everything else. And that implies that if you change one side of a relationship you change both sides (huna.org)

This would relate to Sonja and her father. Both of their lives suffered under the dire circumstances of Sonja's upbringing, but their relationship begins to take a turn as Sonja returns to her homeland as an adult. It is there that both Sonja and her father are able to unite their "hands" physically as they always have been emotionally.

Another insight into the title comes from the author himself during a CNN interview.

But the truth is that these characters, as Dante wrote, were not living, nor yet were they dead; and that their lives are utterly bereft until they managed to manifest the love that they have for one another, and redeem themselves through that love. Until that time, each character knows the sound of one hand clapping, which I take to be an infinite nothingness (Flanagan).

This explanation is slightly different from the Zen teaching, bringing a more realistic spin to the paradox. In his thinking, both hands are silent without each other. In order to be fulfilled, Sonja and her father must find one another. The end is that fulfillment.